Lorentz covariance means that all parts of the equation transform the same.

A rotationally invariant Lagrangian is

tex2html_wrap154 .

examples of scalars:

speed of light: tex2html_wrap155

tex2html_wrap156 is a 4-vector tex2html_wrap157 is a lorentz scalar.

proof: tex2html_wrap158

tex2html_wrap159 is a 1 form. tex2html_wrap160 tex2html_wrap161 tex2html_wrap162 tex2html_wrap163

tex2html_wrap164 tex2html_wrap165 tex2html_wrap166

This implies that the inverse transformation: tex2html_wrap167 so tex2html_wrap168 .(covariant vectors)

contravariant vectors follow tex2html_wrap169 .

tex2html_wrap170 is a lorentz scalar.

source psfile jl@crush.caltech.edu index